Abstract
The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.
Highlights
Patterns of neural activity at the scale of the whole cortex can be quantified by the correlations between the cortical regions
The study of interactions between different cortical regions at rest or during a task has considerably developed in the past decades thanks to progress in non-invasive imaging techniques, such as fMRI, EEG and MEG
These techniques have revealed that distant cortical areas exhibit specific correlated activity during the resting state, called functional connectivity (FC)
Summary
Patterns of neural activity at the scale of the whole cortex can be quantified by the correlations between the cortical regions. EC accounts for mechanisms that determine the synaptic strength (e.g., types and concentration of neurotransmitters), as well as dynamic properties such as neural excitability that may vary with the local activity level and depend on the inputs to the network This means that EC may differ from the anatomical SC obtained from dwMRI. Beyond the analysis of these experimental data, uncovering the relationship between connectivity and activity has attracted much interest recently, with a particular focus for non-trivial connectivity topologies that mimic those observed in the biology [9,10,11,12] Within this field, the inference of the network connectivity from empirically observed activity is an active line of research [1, 13,14,15,16] and is the purpose of the present study
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